It's your router that has the outside IP address, since it's the one that's directly in your ISP's network. This address is shared by all the computers in your home, which are all contained in a separate internal network where internal IP addresses are granted by the router acting as DHCP master. The router acts as a gateway, since your internal home network is otherwise completely cut off from the rest of the world.
When connecting to the exterior, the router acts as your agent and establishes the connection for you, shuttling requests and data between your computer and the outside computer. That means that when connecting to the outside, ALL your internal computers seem to the Internet at large to have the same IP address, which is actually that of your router.
The site What is my IP address will tell you your IP address and explain all the involved concepts.